"'After-birth abortion'" is a term invented by two philosophers, Alberto Giubilini and Francesca Minerva. In the Journal of Medical Ethics, they propose:"
[W]hen circumstances occur after birth such that they would have justified abortion, what we call after-birth abortion should be permissible. … [W]e propose to call this practice ‘after-birth abortion’, rather than ‘infanticide,’ to emphasize that the moral status of the individual killed is comparable with that of a fetus … rather than to that of a child. Therefore, we claim that killing a newborn could be ethically permissible in all the circumstances where abortion would be. Such circumstances include cases where the newborn has the potential to have an (at least) acceptable life, but the well-being of the family is at risk.The writers declare that a newborn infant has no personhood and would not even know s/he was being killed when it happened, so no problem. Kill her and be done with it.
[I]n order for a harm to occur, it is necessary that someone is in the condition of experiencing that harm. If a potential person, like a fetus and a newborn, does not become an actual person, like you and us, then there is neither an actual nor a future person who can be harmed, which means that there is no harm at all. … In these cases, since non-persons have no moral rights to life, there are no reasons for banning after-birth abortions. … Indeed, however weak the interests of actual people can be, they will always trump the alleged interest of potential people to become actual ones, because this latter interest amounts to zero.But as long as we don't call "-cide" it's okay.